Video Transcript
If the pressure of a contained gas
in a tank is 2.3 atmospheres, what is its pressure in centimeters of mercury? Let 𝑃 sub 𝑎 equal 76 centimeters
of mercury. (A) 174.8 centimeters of mercury,
(B) 33.0 centimeters of mercury, (C) 141.8 centimeters of mercury, or (D) 93.1
centimeters of mercury.
To answer this question, we need to
convert the value of the gas pressure from units of atmospheres to units of
centimeters of mercury. We are told that the value of 𝑃
sub 𝑎, which stands for atmospheric pressure, is equal to 76 centimeters of
mercury. This means that in normal
atmospheric pressure, which is equal to one atmosphere, the mercury in a barometer
will be at a height of 76 centimeters. But if the barometer were placed in
a higher-pressure environment, the mercury would rise higher up the tube. This is because there is a greater
pressure pushing down on the mercury in the dish and pushing it up the tube. So, a higher pressure corresponds
to a greater number of centimeters of mercury.
To answer this question, we need to
work out how many centimeters of mercury is equivalent to 2.3 atmospheres.
Let’s start by writing down what we
already know. At atmospheric pressure, the
pressure is equal to one atmosphere, which is equivalent to 76 centimeters of
mercury. In the gas tank, the pressure is
equal to 2.3 atmospheres. In other words, the pressure in the
gas tank is 2.3 times higher than the atmospheric pressure. So, the value of the pressure, when
given in units of centimeters of mercury, must also be 2.3 times higher than at
atmospheric pressure.
So, in units of centimeters of
mercury, the pressure of the gas in the tank is simply equal to 76 centimeters of
mercury multiplied by 2.3. This gives us a pressure of 174.8
centimeters of mercury. So, the correct answer to this
question is option (A).
